Jack (mass 59.0 kg ) is sliding due east with speed 8.00 m/s on the surface of a frozen pond. He collides with Jill (mass 47.0 kg ), who is initially at rest. After the collision, Jack is traveling at 5.00 m/s in a direction 34.0∘ north of east. Ignore friction.
A) What is the direction of the Jill's velocity after the collision?
B) What is the magnitude of the Jill's velocity after the collision?

Explanation:

Traveling at in a direction north of east

Components  north and east

conservation of momentum(mv):

momentum before = momentum after

in the east direction:

Therefore,

east

In the north direction:

At angle,

south of east

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Part(A): The magnitude of Jill's final velocity is .

Part(B): The direction is south to east.

Explanation:

Given:

Mass of Jack,

Mass of Jill,

Initial velocity of Jack,

Initial velocity of Jill,

Final velocity of Jack,

The final angle made by Jack after collision,

Consider that the final velocity of Jill be and it makes an angle of with respect to east, as shown in the figure.

Conservation of momentum of the system along east direction is given by

where, is the component of Jill's final velocity along east. The direction of this component will be along east.

Substituting the value, we have

Conservation of momentum of the system along north direction is given by

where, is the component of Jill's final velocity along north. The direction of this component will be along the opposite to north.

Part(A):

The magnitude of the final velocity of Jill is given by

Part(B):

The direction is given by

answer: 31, 5556. 952 seconds